X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=mpfr%2Fpow_si.c;fp=mpfr%2Fpow_si.c;h=93069057b1d3db8825cf595c2072f2fe29a7ac25;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/mpfr/pow_si.c b/mpfr/pow_si.c new file mode 100644 index 00000000..93069057 --- /dev/null +++ b/mpfr/pow_si.c @@ -0,0 +1,245 @@ +/* mpfr_pow_si -- power function x^y with y a signed int + +Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao projects, INRIA. + +This file is part of the GNU MPFR Library. + +The GNU MPFR Library is free software; you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 2.1 of the License, or (at your +option) any later version. + +The GNU MPFR Library is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public +License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with the GNU MPFR Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, +MA 02110-1301, USA. */ + +#define MPFR_NEED_LONGLONG_H +#include "mpfr-impl.h" + +/* The computation of y = pow_si(x,n) is done by + * y = pow_ui(x,n) if n >= 0 + * y = 1 / pow_ui(x,-n) if n < 0 + */ + +int +mpfr_pow_si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd) +{ + MPFR_LOG_FUNC (("x[%#R]=%R n=%ld rnd=%d", x, x, n, rnd), + ("y[%#R]=%R", y, y)); + + if (n >= 0) + return mpfr_pow_ui (y, x, n, rnd); + else + { + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + if (MPFR_IS_NAN (x)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + else if (MPFR_IS_INF (x)) + { + MPFR_SET_ZERO (y); + if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0) + MPFR_SET_POS (y); + else + MPFR_SET_NEG (y); + MPFR_RET (0); + } + else /* x is zero */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (x)); + MPFR_SET_INF(y); + if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0) + MPFR_SET_POS (y); + else + MPFR_SET_NEG (y); + MPFR_RET(0); + } + } + MPFR_CLEAR_FLAGS (y); + + /* detect exact powers: x^(-n) is exact iff x is a power of 2 */ + if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0) + { + mp_exp_t expx = MPFR_EXP (x) - 1, expy; + MPFR_ASSERTD (n < 0); + /* Warning: n * expx may overflow! + * Some systems (apparently alpha-freebsd) abort with + * LONG_MIN / 1, and LONG_MIN / -1 is undefined. + * Proof of the overflow checking. The expressions below are + * assumed to be on the rational numbers, but the word "overflow" + * still has its own meaning in the C context. / still denotes + * the integer (truncated) division, and // denotes the exact + * division. + * - First, (__gmpfr_emin - 1) / n and (__gmpfr_emax - 1) / n + * cannot overflow due to the constraints on the exponents of + * MPFR numbers. + * - If n = -1, then n * expx = - expx, which is representable + * because of the constraints on the exponents of MPFR numbers. + * - If expx = 0, then n * expx = 0, which is representable. + * - If n < -1 and expx > 0: + * + If expx > (__gmpfr_emin - 1) / n, then + * expx >= (__gmpfr_emin - 1) / n + 1 + * > (__gmpfr_emin - 1) // n, + * and + * n * expx < __gmpfr_emin - 1, + * i.e. + * n * expx <= __gmpfr_emin - 2. + * This corresponds to an underflow, with a null result in + * the rounding-to-nearest mode. + * + If expx <= (__gmpfr_emin - 1) / n, then n * expx cannot + * overflow since 0 < expx <= (__gmpfr_emin - 1) / n and + * 0 > n * expx >= n * ((__gmpfr_emin - 1) / n) + * >= __gmpfr_emin - 1. + * - If n < -1 and expx < 0: + * + If expx < (__gmpfr_emax - 1) / n, then + * expx <= (__gmpfr_emax - 1) / n - 1 + * < (__gmpfr_emax - 1) // n, + * and + * n * expx > __gmpfr_emax - 1, + * i.e. + * n * expx >= __gmpfr_emax. + * This corresponds to an overflow (2^(n * expx) has an + * exponent > __gmpfr_emax). + * + If expx >= (__gmpfr_emax - 1) / n, then n * expx cannot + * overflow since 0 > expx >= (__gmpfr_emax - 1) / n and + * 0 < n * expx <= n * ((__gmpfr_emax - 1) / n) + * <= __gmpfr_emax - 1. + * Note: one could use expx bounds based on MPFR_EXP_MIN and + * MPFR_EXP_MAX instead of __gmpfr_emin and __gmpfr_emax. The + * current bounds do not lead to noticeably slower code and + * allow us to avoid a bug in Sun's compiler for Solaris/x86 + * (when optimizations are enabled). + */ + expy = + n != -1 && expx > 0 && expx > (__gmpfr_emin - 1) / n ? + MPFR_EMIN_MIN - 2 /* Underflow */ : + n != -1 && expx < 0 && expx < (__gmpfr_emax - 1) / n ? + MPFR_EMAX_MAX /* Overflow */ : n * expx; + return mpfr_set_si_2exp (y, n % 2 ? MPFR_INT_SIGN (x) : 1, + expy, rnd); + } + + /* General case */ + { + /* Declaration of the intermediary variable */ + mpfr_t t; + /* Declaration of the size variable */ + mp_prec_t Ny; /* target precision */ + mp_prec_t Nt; /* working precision */ + mp_rnd_t rnd1; + int size_n; + int inexact; + unsigned long abs_n; + MPFR_SAVE_EXPO_DECL (expo); + MPFR_ZIV_DECL (loop); + + abs_n = - (unsigned long) n; + count_leading_zeros (size_n, (mp_limb_t) abs_n); + size_n = BITS_PER_MP_LIMB - size_n; + + /* initial working precision */ + Ny = MPFR_PREC (y); + Nt = Ny + size_n + 3 + MPFR_INT_CEIL_LOG2 (Ny); + + MPFR_SAVE_EXPO_MARK (expo); + + /* initialise of intermediary variable */ + mpfr_init2 (t, Nt); + + /* We will compute rnd(rnd1(1/x) ^ |n|), where rnd1 is the rounding + toward sign(x), to avoid spurious overflow or underflow, as in + mpfr_pow_z. */ + rnd1 = MPFR_EXP (x) < 1 ? GMP_RNDZ : + (MPFR_SIGN (x) > 0 ? GMP_RNDU : GMP_RNDD); + + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + MPFR_BLOCK_DECL (flags); + + /* compute (1/x)^|n| */ + MPFR_BLOCK (flags, mpfr_ui_div (t, 1, x, rnd1)); + MPFR_ASSERTD (! MPFR_UNDERFLOW (flags)); + /* t = (1/x)*(1+theta) where |theta| <= 2^(-Nt) */ + if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags))) + goto overflow; + MPFR_BLOCK (flags, mpfr_pow_ui (t, t, abs_n, rnd)); + /* t = (1/x)^|n|*(1+theta')^(|n|+1) where |theta'| <= 2^(-Nt). + If (|n|+1)*2^(-Nt) <= 1/2, which is satisfied as soon as + Nt >= bits(n)+2, then we can use Lemma \ref{lemma_graillat} + from algorithms.tex, which yields x^n*(1+theta) with + |theta| <= 2(|n|+1)*2^(-Nt), thus the error is bounded by + 2(|n|+1) ulps <= 2^(bits(n)+2) ulps. */ + if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags))) + { + overflow: + MPFR_ZIV_FREE (loop); + mpfr_clear (t); + MPFR_SAVE_EXPO_FREE (expo); + MPFR_LOG_MSG (("overflow\n", 0)); + return mpfr_overflow (y, rnd, abs_n & 1 ? + MPFR_SIGN (x) : MPFR_SIGN_POS); + } + if (MPFR_UNLIKELY (MPFR_UNDERFLOW (flags))) + { + MPFR_ZIV_FREE (loop); + mpfr_clear (t); + MPFR_LOG_MSG (("underflow\n", 0)); + if (rnd == GMP_RNDN) + { + mpfr_t y2, nn; + + /* We cannot decide now whether the result should be + rounded toward zero or away from zero. So, like + in mpfr_pow_pos_z, let's use the general case of + mpfr_pow in precision 2. */ + MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_SIGN (x), + MPFR_EXP (x) - 1) != 0); + mpfr_init2 (y2, 2); + mpfr_init2 (nn, sizeof (long) * CHAR_BIT); + inexact = mpfr_set_si (nn, n, GMP_RNDN); + MPFR_ASSERTN (inexact == 0); + inexact = mpfr_pow_general (y2, x, nn, rnd, 1, + (mpfr_save_expo_t *) NULL); + mpfr_clear (nn); + mpfr_set (y, y2, GMP_RNDN); + mpfr_clear (y2); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_UNDERFLOW); + goto end; + } + else + { + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_underflow (y, rnd, abs_n & 1 ? + MPFR_SIGN (x) : MPFR_SIGN_POS); + } + } + /* error estimate -- see pow function in algorithms.ps */ + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - size_n - 2, Ny, rnd))) + break; + + /* actualisation of the precision */ + MPFR_ZIV_NEXT (loop, Nt); + mpfr_set_prec (t, Nt); + } + MPFR_ZIV_FREE (loop); + + inexact = mpfr_set (y, t, rnd); + mpfr_clear (t); + + end: + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd); + } + } +}